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<article class="li"><h4 class="heading">
<span class="type">Item</span><span class="space"> </span><span class="codenumber">4</span><span class="period">.</span>
</h4>
<p>By interpreting the step function <span class="process-math">\(u(t-1)\)</span> up to and after <span class="process-math">\(t=1,\)</span> show that the impulse at <span class="process-math">\(t=1\)</span> produces what you would expect: a discontinuity in <dfn class="terminology">velocity</dfn> at <span class="process-math">\(t=1.\)</span> Sketch the full solution:</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
y(t)
=5t^2 \ \ {\rm for} \ t\leq 1 \ \ \ \ \ ({\rm so \ here} \ y'(t)=10t)
\end{equation*}
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<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
y(t) =5t^2 + 10(t-1)\ \ {\rm for} \ t&gt; 1 \ \ \ \
({\rm  so \ here} \ y'(t) =10t +10) .
\end{equation*}
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